If `sinalpha=x and tan alpha=y,` prove that, `1/x^2-1/y^2=1`.

If (2sinalpha)/(1+cosalpha +sinalpha)=y , then prove that (1-cosalpha+sinalpha )/(1+sinalpha) is also equal to y.

If (2sinalpha)/(1+cosalpha+sinalpha)=y , then prove that (1-cosalpha+sinalpha)/(1+sinalpha) is also equal to y.

If (2sinalpha)/(1+cosalpha +sinalpha)=y , then prove that (1-cosalpha+sinalpha )/(1+sinalpha) is also equal to y.

If x=tan t and y=tan pt , prove that, (1+x^(2))y_(2)+2(x-py)y_(1)=0

If y = tan^(-1) x, prove that (1 + x^2)y_2 + 2xy_1 = 0

If y=tan x, prove that y_(2)=2yy_(1)

If sinalpha+cos alpha=sqrt2 cos alpha then prove that tan 2alpha=1

If tan x = tan y cos2 alpha prove that: tan (yx) = (tan ^ (2) alpha * sin2y) / (1 + tan ^ (2) alpha * cos2y)

If y=e^(tan^-1x), prove that (1+x^2)y_2+(2x-1)y_1=0

If y=e^(tan^(-1)x) , prove that (1+x^2)y_2+(2x-1)y_1=0 .